Polyalkylene glycol-based polymers are useful polymers used in various industrial fields, and have high performance when used, for example, in dispersants, detergent compositions, and the like in aqueous environment. In the case that polyalkylene glycol-based polymers are used in aqueous environment, several influential factors such as the quality of water to be used and the interaction with other materials used in combination should be considered. Specifically, the hardness of water is different among countries or regions, and some of polyalkylene glycol-based polymers that produce various effects in aqueous environment with low water hardness may not produce sufficient effects in aqueous environment with high water hardness. When used, for example, in a detergent composition containing a surfactant, some polyalkylene glycol-based polymers may not have sufficient washing performance depending on the degree of the interaction with the surfactant.
Examples of conventional polyalkylene glycol-based polymers include copolymers produced from 40 to 99.5 mol % of a specific unsaturated carboxylic acid-based monomer, 0.5 to 60 mol % of an unsaturated alcohol-based monomer represented by the formula (P-1), and 0 to 40 mol % of a monomer copolymerizable with these monomers (see Patent Document 1). Patent Document 1 teaches that these copolymers have high ability to disperse carbon black and the chelate effect and therefore can be used as detergent builders.

In the formula, R1 and R2 independently represent H or a methyl group, and at least one of R1 and R2 is not a methyl group; R3 represents —CH2—, —(CH2)2—, or —C(CH3)2—; the total sum of the numbers of carbons in R1, R2, and R3 is 3; Y represents C2-3 alkylene group; and n is an integer of from 0 to 100. The copolymers are known to be suitable as dispersants for satin white (calcium sulfoaluminate hexahydrate) (see Patent Document 2).
Other examples of conventional polyalkylene glycol-based copolymers include soluble copolymers obtained by copolymerizing monomer materials essentially containing a specific unsaturated carboxylic acid-based monomer and an unsaturated alcohol-based monomer represented by the formula (P-2) (see Patent Document 3). Patent Document 3 teaches that these copolymers are suitably used in liquid detergent compositions because of their excellent washing performance such as high anti-soil redeposition ability and compatibility with surfactants.

In the formula, R1, R2, and R4 independently represent H or a methyl group, and at least one of R1 (or R4) and R2 is not a methyl group; R3 represents —CH2—, —(CH2)2—, or —C(CH3)2—; the total sum of the numbers of carbons in R1, R2, R3, and R4 is 3; Y represents a C2-18 alkylene group; and n is an integer of from 1 to 300.
In addition, polyalkylene glycol-based polymer compositions are disclosed (see Patent Document 4). These polyalkylene glycol-based polymer compositions have a sulfur oxoacid group at an end and are prepared by copolymerizing a (meth)acrylic acid-based monomer, an unsaturated polyalkylene glycol-based monomer having 6 to 300 polyalkylene oxide repeating units, and a monoethylenic unsaturated monomer copolymerizable with these monomers, and have an introduced sulfur amount S ((amount of S in polymer)/(total S amount)×100) of not less than 3. Patent Document 4 teaches that these polymer compositions are excellent in the calcium capturing ability, clay dispersibility, and anti-gelling property and therefore can be suitably used as detergent builders and the like.